In this work, using the ProtonDecay package [1]}, we investigate the nucleon decay rates for these 13 decay channels in two “toy models” (following [2]}, [3]}) which both realize the GUT scale ratios \(y_\tau /y_b=3/2\)  and \(y_\mu /y_s=9/2\) , but feature a different flavor structure in the Yukawa matrices. Both models are SU(5) GUT scenarios with a Higgs sector consisting of the representations 5, 24 and 45,A model with this field content but different predictions for the GUT scale Yukawa ratios has been proposed in [4]}. A lower bound of \(1\times 10^{-68}\)  GeV for the total proton decay rate was later given in [5]}, [6]},
however not in the here considered scenario with predicted Yukawa ratios and specified flavor structures. such that the GUT operators leading to both relations can be realized. In addition, to explain the observed neutrino masses via the type I seesaw mechanism, extra fermionic SU(5) singlet representations are added.
We perform Markov Chain Monte Carlo (MCMC) analyses in order to confront the models with the available experimental data. As we will show, if several nucleon decay channels are observed, the ratios between their partial decay rates can serve as “fingerprints”, allowing to separate between the two “toy models”.
